Question

exercitiul 16 va rog​

Answer 1

Răspuns:

Explicație pas cu pas:

a) lim x->inf(x -lnx) =  lim x->inf(ln(e^x) -lnx) =

lim x->inf(ln(e^x/x) ) = inf

b)  lim x->0(x -lnx) =

lim x->inf(ln(e^x/x) ) =

lim x->inf(ln(e^0/0) ) = 1/0 = inf

x = 0 asimpt. verticala

Nu are asimpt. orizontala ( lim x->inf f(x) = inf)

y = mx +n  ec. asimpt. oblice

m = lim x->inf(f(x)/x) = lim x->inf(1 -lnx/x) = 1

n = lim x->inf(f(x) -mx) =

lim x->inf(x -lnx -x) =

lim x->inf( -lnx) = -inf

Nu are asimpt. oblica